Underground reservoirs may contain hydrocarbons having a viscosity in excess of approximately 100 cP at reservoir temperature. The testing operations (e.g., fluid sampling) in such reservoirs may benefit from the mobility of the hydrocarbon being reduced prior to or during hydrocarbon extraction from the reservoir. In some cases (e.g., the reservoir contains hydrocarbons that are liquids at reservoir temperature, that is, the hydrocarbons have a viscosity value lower than about 10,000 cP), the mobilization of reservoir fluids may be effected by increasing locally the formation temperature close to a sampling port. Increasing the formation temperature reduces the viscosity and results in a more mobile fluid, and thereby expediting testing operations.
For all forms of heating, there is limited power available downhole, for example, on the order of 10 kW. If thermal convection in the wellbore is low, this power may be sufficient compared to the power required to increase the temperature of a formation. For example, in the absence of heat convection in the wellbore, prior results indicate that a resistive heater forced to contact the wellbore wall and having a power of about 0.5 kW may elevate the formation fluid temperature locally by about 100° C. without giving rise to significant thermal degradation of the hydrocarbon.
In some cases, however, heat convection may be significant and may even prevent adequate heat transfer to the formation. Indeed, the convection may lead to significant loss of heat in the wellbore fluid, away from the zone of the formation to be heated. This may be particularly the case when using surface heating wherein heat may be transferred from a hot surface provided by a downhole testing tool, through the wellbore fluid, and to the formation. Heat convection may also be particularly significant in vertical wells. It will be appreciated that vertical uncased wells are more prevalent than horizontal and cased holes during exploration and appraisal stages of hydrocarbon reservoir evaluation, particularly in the case of heavy oil reservoirs which may be found within less than 1000 m of the surface.
The propensity for natural convection may be determined by the Grashof number, which approximates the ratio of the buoyancy to viscous force acting on a fluid. The Grashof number Gr is defined by Equation 1 below:
                              G          r                =                                                            g                ⁡                                  (                                                            T                      heater                                        -                                          T                      res                                                        )                                            ⁢                              L                2                                                                    〈                η                〉                            2                                ⁢                      {                                          -                                  1                  ρ                                            ⁢                                                (                                                            ∂                      ρ                                                              ∂                      T                                                        )                                p                                      }                                              Equation        ⁢                                  ⁢        1            
In Equation 1, g is the acceleration of free-fall and is a constant. As indicated by Equation 1, the propensity for natural convection depends on the physical properties of the wellbore fluid, which will presumably be some form of drilling lubricant, through <η> the mean kinematic viscosity of the wellbore fluid over the temperature range, and through <−1/ρ (∂ρ/∂T)p> the mean volumetric thermal expansion of the wellbore fluid over the temperature range. As indicated by Equation 1, the propensity for natural convection also depends on the heating configuration through Theater and Tres, the temperatures of the heater and wellbore above (which is essentially equal to the reservoir), respectively, and through L, a characteristic length, for example the distance between the heater and the formation. For a reservoir at a temperature of 20° C. and at and a pressure of 14 MPa, and for a heater at a temperature of 120° C., the values of the Grashof number taken for water- and oil-based muds suggest the buoyancy force is sufficient for significant convection in the wellbore. Convection may in turn lead to a significant energy loss into the wellbore fluid.